Weak solutions to the equations of motion for compressible magnetic fluids (Q1019131)

The authors study flows of compressible magnetic ferrofluids. The system to be solved is the barotropic Navier-Stokes system in \({\mathbb R}^3\) including an angular momentum equation, coupled to an equation for magnetization and magnetostatic equations. The unknowns are the density \(\varrho\), the velocity \(\vec{v}\), the angular momentum \(\Omega\) and the magnetization \(M\). The state function fixing the model is the pressure \(p(\varrho,M)=p_e(\rho)+p_m(M)\), and all the other physical parameters are supposed to be positive constants. The problem is posed in a bounded domain with smooth boundary of class \(C^{2+r}\), \(r>0\). Weak solutions in the renormalized sense are proved to exist globally in time (renormalized density and zero velocity in vacuum zones). The proof is an extension of Lions-Feireisl method of regularization, Galerkin approximation and weak limits techniques.